(CNN) -- A 4-month-old baby boy from Grain Valley, Missouri, was in critical condition after a family pet ferret ate seven of the infant's fingers, and the boy's parents are under investigation for neglect and failure to obtain a $100 license for the exotic pet, police chief Aaron Ambrose told CNN Tuesday.

Authorities are not releasing the names of the baby or his parents, Ambrose said.

The mother was awakened at 2:30 a.m. Monday to her baby's crying, and she awakened her husband with screams upon discovering what happened, Ambrose said.

The dad killed the pet by hurling it across the house, Ambrose said.

The baby now has only two thumbs and a partial pinkie, the chief said. The ferret was about six months old, a police report said.

"It's very unusual, there's no doubt about it," Ambrose said of the incident.

Ambrose said he believed the ferret was a young animal recently acquired by the family.

"We're trying to figure out if this thing had a crate or a cage, or was it running around the house," Ambrose said. "It jumped into the rocker thing that the baby was sleeping in and ate seven of its fingers."

The parents said "they never heard the baby crying" until late into the ordeal, Ambrose said. "Who knows what's going on there. These are all things we're working on now -- where they were sleeping and where the baby was in conjunction with them."

Upon seeing the ferret, the father "just grabbed it and threw it," Ambrose said. "It hit a dishwasher or cabinet or something like that."

A necropsy is being performed on the ferret to examine its stomach contents and determine whether the animal had rabies, Ambrose said.

A law enforcement colleague with ties to Shriners International, a philanthropy known for working with child burn victims, called Ambrose upon hearing the news and made him aware of a procedure in which some toes can be surgically removed and attached to the hands in place of fingers, Ambrose said.

Ambrose said he wasn't aware Tuesday of whether the family was made aware of the Shriner's interest in baby's case. The baby is the care of Children's Mercy Hospital in Kansas City, Missouri, which is 25 miles west of Grain Valley, Ambrose said.

"They can take the child's toes, like two per foot, and attach them to the hands and elongate them where they become like fingers," Ambrose said. "It's all free and it's through the Shriners.

"It's nice to know there are options out there. He can somewhat of a normal life as far as using his hands," Ambrose said.

In the recent past, animal control officers responded to complaints about the family's dogs, including a Rottweiler, Ambrose said.

"They have had other animal issues with dogs for licensing and things like that," Ambrose said, adding that a dog license costs $10 or so in Grain Valley. "There was a concern back in the summer about barking dogs and...the way they were keeping the animals."

In the wake of the most recent incident, ferret activists and rescuers from around the country have called Ambrose about the pet.

"We've had them calling from all sorts of states asking about the ferret," Ambrose said. "Well, I guess if you collect dead ferrets, you can have one."

Ambrose said parents should examine safety about pets.

"If you have a baby or children, if you have animals, I would assume you want to educate yourself on the animal," Ambrose said. "Are they good around kids? Hopefully, people will take a general look at this and see what's the lesson."